Answer:
1. F(x) only-----------------------
F(x) is in the format of a quadratic function:
y = ax² + bx + c, with a = - 1, b = 0, c = 5Hence it is a parabola.
The table represents a relation with two x-intercepts and two y-intercepts (points with the coordinate of 0).
We know that parabola can have maximum of one y-intercept, hence G(x) is not a parabola.
The matching answer choice is the first one.
Carl takes out a loan which accrues interest at a flat rate of 1.96% per quarter.
what is the equivalent yearly simple interest rate?
Carl will be charged 7.84% of the initial loan amount as interest.
When taking out a loan, it's important to understand the interest rate and how it will affect the total amount you will owe. In this case, Carl's loan accrues interest at a flat rate of 1.96% per quarter. This means that every quarter, Carl will be charged 1.96% of the initial loan amount as interest.
To determine the equivalent yearly simple interest rate, we use the formula: Yearly interest rate = Quarterly interest rate x 4. This formula works because there are four quarters in a year, so we can multiply the quarterly interest rate by four to get the annual interest rate.
In this case, the quarterly interest rate is 1.96%. Multiplying this by four, we get an annual interest rate of 7.84%. This means that over the course of a year, Carl will be charged 7.84% of the initial loan amount as interest.
Understanding the interest rate is important because it can significantly impact the total amount that you will owe on a loan. A higher interest rate means that you will pay more in interest over the life of the loan, which can make the loan more expensive overall.
By calculating the equivalent yearly simple interest rate, Carl can better understand how much he will owe in interest over the course of the loan and make an informed decision about whether or not to take out the loan.
To learn more about loan refer here:
https://brainly.com/question/30015539
#SPJ11
2. A manufacturer of electronic kits has found that the mean time required for novices to assemble its new circuit tester is 3. 15 hours, with a sample standard deviation of 0. 23 hours. A consultant has developed a new instructional booklet intended to reduce the time an inexperienced kit builder will need to assemble the device. In a test of the effectiveness of the new booklet, 25 novices require a mean of 2. 98 hours to complete the job. Assuming the population of times is normally distributed, and using the 0. 01 level of significance, should we conclude that the new booklet is effective? Determine and interpret the p-value for the test
Assuming the population of times is normally distributed, and using the 0. 01 level of significance, we can conclude that the new booklet is effective.
To determine if the new instructional booklet is effective in reducing the assembly time for novices, we will perform a one-sample t-test using the given information.
1. State the null hypothesis (H0) and the alternative hypothesis (H1):
H0: There is no difference in the mean assembly time with the new booklet (µ = 3.15 hours).
H1: The mean assembly time with the new booklet is less than 3.15 hours (µ < 3.15 hours).
2. Identify the level of significance, sample size, sample mean, and sample standard deviation:
α = 0.01
n = 25
x = 2.98 hours
s = 0.23 hours
3. Calculate the test statistic:
t = (x - µ) / (s / √n) = (2.98 - 3.15) / (0.23 / √25) = -0.17 / 0.046 = -3.70
4. Find the p-value for the test:
Using a t-distribution table or calculator, the p-value for a one-tailed test with t = -3.70 and degrees of freedom (df) = 24 is approximately 0.0005.
5. Compare the p-value with the level of significance:
Since the p-value (0.0005) is less than α (0.01), we reject the null hypothesis.
Based on the p-value, we have enough evidence to conclude that the new instructional booklet is effective in reducing the assembly time for novices at the 0.01 level of significance.
Learn more about Level of significance:
https://brainly.com/question/30542688
#SPJ11
You are making a 3 foot by 3 foot coffee table with a glass top surrounded by a cherry border of uniform width. The cherry border is included in the 3 x 3 measurements. You have 5 square feet of cherry border. What should the width of the border be?
Answer:
Step-by-step explanation:
The total area of the coffee table (including the cherry border) is:
3 feet x 3 feet = 9 square feet
We know that the area of the cherry border is:
5 square feet
To find the width of the cherry border, we need to subtract the area of the glass top from the total area of the coffee table:
9 square feet - area of glass top = area of cherry border
The area of the glass top is:
(3 feet - 2x) x (3 feet - 2x)
where x is the width of the cherry border.
Since the glass top is square, we can set the two dimensions equal to each other:
(3 feet - 2x) = (3 feet - 2x)
Expanding the left-hand side, we get:
9 feet - 6x = 9 feet - 6x
Simplifying, we get:
0 = 0
This means that the width of the cherry border does not affect the area of the glass top. Therefore, we can set the area of the glass top equal to the total area of the coffee table minus the area of the cherry border:
(3 feet - 2x) x (3 feet - 2x) = 9 square feet - 5 square feet
Simplifying, we get:
(3 feet - 2x) x (3 feet - 2x) = 4 square feet
Expanding the left-hand side, we get:
9 feet^2 - 12 feet x + 4x^2 = 4 square feet
Subtracting 4 square feet from both sides, we get:
9 feet^2 - 12 feet x + 4x^2 - 4 square feet = 0
Simplifying, we get:
4x^2 - 12 feet x + 9 feet^2 - 4 square feet = 0
Using the quadratic formula, we get:
x = [12 feet ± sqrt((12 feet)^2 - 4(4)(9 feet^2 - 4 square feet))] / (2(4))
Simplifying, we get:
x = [12 feet ± sqrt(144 feet^2 - 4(4)(9 feet^2 - 4 square feet))] / 8
x = [12 feet ± sqrt(144 feet^2 - 144 feet^2 + 64 square feet)] / 8
x = [12 feet ±
solve the equation sin theta equals to Cos 35
Answer:
55 degrees
Step-by-step explanation:
sin Φ = cos 35
sin Φ = .81915
Φ = arc sin (.81915) = 55 degrees
Or you could just know that the cos of an angle is equal to the sin of its comeplement
A 32" flat screen television measures 32 inches across its diagonal. the diagonal makes a 35° angle with the bottom of the television
32"
h
a
35°
select all equations that can be used to solve for the height, h, of the television screen
The trignometric equation h = (32 inches) x tan(35°) can be used to solve for the height, h, of the television screen.
We can use trigonometry to solve for the height, h, of the television screen. From the given information, we can form a right triangle with the diagonal of the television screen as the hypotenuse, and the height of the screen as one of the legs.
Since we are given the angle between the diagonal and the bottom of the television, we can use the trigonometric function tangent to relate the height and the diagonal.
The equation we can use to solve for the height is:
tan(35°) = [tex]\frac{h }{ (32 inches)}[/tex]
Rearranging this equation, we get:
h = (32 inches) x tan(35°)
Therefore, the equation that can be used to solve for the height, h, of the television screen is:
h = (32 inches) x tan(35°)
So, the equation h = (32 inches) x tan(35°) can be used to solve for the height, h, of the television screen.
To learn more about trignometry refer here:
https://brainly.com/question/22986150
#SPJ11
Given m||n, find the value of x
Answer:
x=32°
Step-by-step explanation:
3x-2=2x+30
x-2=30
x=32°
Find the volume of a pyramid whose base is a square with side lengths of 6 units and height of 8 units.
Answer:
i think the answer is 96
Step-by-step explanation:
This equation gives the light intensity, I (in lumens), in water at a depth of feet: d= -425log(I/12). I) What is the intensity of the light at a depth of 300 feet? Please show all work. Ii) At what water depth is the intensity 5 lumens? Please show all work. Iii) What is the light intensity at the surface of the water? Please show all work
i) The light intensity at a depth of 300 feet is approximately 0.131 lumens.
ii)The light intensity of 5 lumens is reached at a depth of approximately 106.6 feet.
iii)The light intensity at the surface of the water is 12 lumens.
The equation given is:
[tex]d= -425log(\frac{I}{12} )[/tex]
where d is the depth in feet, and l is the light intensity in lumens.
i)To find the intensity of light at a depth of 300 feet:
[tex]d= -425log(\frac{I}{12} )[/tex]
[tex]or, \frac{d}{-425}=log(\frac{I}{12})[/tex]
[tex]or, 10^{\frac{d}{-425}}=\frac{I}{12}[/tex]
[tex]or, 12 X 10^{\frac{d}{-425}}=I[/tex]
Given, d= 300 feet. Hence,
[tex]or, 12 X 10^{\frac{300}{-425}}=I[/tex]
or, I = 0.131 lumens (approx.)
ii) We have been given the equation :
[tex]d= -425log(\frac{I}{12} )[/tex]
when I =5 lumens
[tex]d= -425log(\frac{5}{12} )[/tex]
or, d = 106.6 feet (approx.)
iii) For finding the light intensity at the surface of the water d=0
[tex]d= -425log(\frac{I}{12} )[/tex]
Putting d = 0 we get
[tex]0= -425log(\frac{I}{12} )[/tex]
[tex]or, log(\frac{I}{12})=0[/tex]
[tex]or, \frac{I}{12} = 10^0 = 1[/tex]
or, I = 12 lumens
Therefore the light intensity at the surface of the water is 12 lumens.
To know about light intensity:
brainly.com/question/30499504
#SPJ4
1.Number graph
2.Graph the line using the equation y=1/2x
The equation y=1/2x can be graphed using either number graph or the slope-intercept form. In either case, the result is a straight line that passes through the same points.
What is number graph?In mathematics, a graph is a visual representation of a mathematical relationship. The equation y=1/2x is a linear equation, which means that it describes a straight line. This equation can be graphed using the number graph.
To graph the equation y=1/2x, one must first plot points on the graph. To do this, one can use the given equation to calculate the x and y values of the points. For example, if x is equal to 1, then y is equal to 1/2. Therefore, the point (1, 1/2) can be plotted on the graph. This process can be repeated for other values of x, such as 2, 3, and 4. The result is a straight line that passes through the points (1, 1/2), (2, 1), (3, 1 1/2), and (4,2).
The equation y=1/2x can also be graphed using the slope-intercept form of the equation. This form of the equation is written as y=mx + b, where m is the slope of the line and b is the y-intercept. For the equation y=1/2x, the slope is 1/2 and the y-intercept is 0. To graph the line, one must first plot the y-intercept, which is the point (0,0). Then, one must calculate the slope and draw a line through (0,0) in the direction of the slope. The result is a straight line that passes through the points (0, 0), (1, 1/2), (2,1), (3, 1 1/2), and (4, 2).
In conclusion, the equation y=1/2x can be graphed using either number graph or the slope-intercept form. In either case, the result is a straight line that passes through the same points.
To know more about graph click-
http://brainly.com/question/19040584
#SPJ1
The slope-intercept form or a number graph can both be used to visualise the equation y=1/2x. The outcome is a straight line that goes through the same spots in both scenarios.
What is number graph?A graph in mathematics is a picture of a mathematical connection. A linear equation is one that describes a straight line, such as y=1/2x. The number graph can be used to graph this equation.
The graph must first have points drawn on it before the equation y=1/2x can be graphed. To do this, one can compute the x and y values of the points using the above equation. For instance, y is equal to 1/2 if x is equal to 1. As a result, the graph's point (1, 1/2) can be drawn. You can repeat this procedure for x values of 2, 3, and 4. Consequently, a straight line that traverses the coordinates (1, 1/2), (2, 1), (3, 1 1/2),and (4,2).
The slope-intercept form of the equation can also be used to graph the equation y=1/2x. Y=mx + b, where m is the line's slope and b is its y-intercept, is how this form of the equation is expressed. The slope and y-intercept of the equation y=1/2x are 1/2 and 0, respectively.
Plotting the y-intercept, or the point, is required before the line can be graphed. (0,0). The next step is to determine the slope and draw a line through (0,0) in the slope's direction. A straight line is created as a result, passing through the points (0, 0), (1, 1/2), (2, 1), (3, 1 1/2), and (4, 2).
In conclusion, the slope-intercept form or a number graph can both be used to graph the equation y=1/2x. The outcome is a straight line that goes through the same spots in both scenarios.
To know more about graph, click-
brainly.com/question/19040584
#SPJ9
Simplify m^8m^−6.
one over m to the forty eighth power
m^2
one over m squared
−m^14
It should be noted that m⁸m⁻⁶ is equivalent to (m²)¹, which is equal to m².
How to calculate the valueUsing the product of powers rule for exponents, we can simplify m⁸m as follows:
m⁸m⁻⁶ = m⁸⁻⁶) = m²
Therefore, m⁸⁻⁶ is equal to m².
Now, we can further simplify by expressing m² as (m²)¹. Multiplying the exponents, we get:
(m²)¹ = m²
We can say that m⁸m⁻⁶ is equivalent to (m²)¹, which is equal to m².
Leans more about exponents on
https://brainly.com/question/13669161
#SPJ1
Select the correct answer.
In a sequence described by a function, what does the notation f(3) = 1 mean?
O A.
The third term in the sequence has a value of 1.
OB.
The first term in the sequence has a value of 3.
OC. The common difference of the sequence is 3.
OD. The common ratio of the sequence is 3.
The third term in the sequence has a value of 1.
Here, we have,
Sequence
Given:
f(3) = 1
Let f(x) b a function.
Here x is replaced by "3", f(3) represents the value of the 3rd term of the function, which is 1.
In this case f(3) = 1 means the value of a member of the sequence when x = 3 is 1.
For example, if the sequence is the values of x^2-8 from 1 to infinity, then f(1) would have a value 1-8 = -7 and f(3) would be 9- 8 = 1
The third term in the sequence has a value of 1.
To learn more about the sequence
brainly.com/question/17902194
#SPJ1
Can someone help me with this, please?
Answer:
You are correct.
Hope this helps!
Step-by-step explanation:
The lines intersect at one point and that is the solution.
( The image shows a graph with infinite solutions. ( ignore the Byjus thing i was just trying to find an image that showed an example ... ) )
What is the surface of the prism
Answer:
The third answer is correct
Step-by-step explanation:
Given:
A net of a rectangular prism
l (length) = 11,75 cm
w (width) = 5,75 cm
h (height) = 4 cm
Find: A (surface area) - ?
The surface area is equal to the sum of the areas of all the sides
There are:
2 sides with dimensions of 11,75 cm and 4 cm
2 sides with dimensions of 5,75 cm and 11,75 cm
2 sides with dimensions of 4 cm and 5,75 cm
[tex]a(surface) = 4 \times 11.75 \times 2 + 5.75 \times 11.75 \times 2 + 4 \times 5.75 \times 2 = 275.125 = 275 \frac{1}{8} \: {cm}^{2} [/tex]
A zebra crossing has alternating white and black stripes, each 50 cm wide. The first stripe is white and the last one is white. The zebra crossing in front of our school has 8 white stripes. How wide is the road? A) A 7m 7,5m © 8m 8m 0 8,5m E 9m
The road with alternating white and black stripes and each 50 cm wide is 7.5 m wide.
The road consists of alternating white and black stripes
No. of white stripes = 8
As the first and last stripe is white so in between the black stripes will be 7
No. of black stripes = 7
Total no. of stripes = 15
Width of black stripe = 50 cm
Width of white stripe = 50 cm
Width of whole road = total no. of stripes × width of each stripe
Width of whole road = 15 × 50
Width of whole road = 750 cm
To convert m into cm
Now, 1 m = 100 cm
1 cm = 1/100 m
750 cm = 750/100 m
750 cm = 7.5 m
Hence the width of the road is 7.5 m
To know more about Wide click here :
https://brainly.com/question/30295979
#SPJ4
Use the following bond listing for Pacific Bell to answer the following: Bonds Cur. Yia. Vol Close Net. Chg. 5 6. 55 5 1 1 Pac Bell 6– 34 99- 4 8 What is the coupon rate and maturity date for this bond? 5 The coupon rate is 62, the maturity date is 2034. A. B 1 The coupon rate is 8 the maturity date is 2034. 5 The coupon rate is 6. The maturity date is 2099. D. The coupon rate is 6. 55; the maturity date is in 5 years.
The coupon rate for this Pacific Bell bond is 6%, and the maturity date is in 2034. So, the correct option is B: The coupon rate is 6%, and the maturity date is 2034.
The information provided in the bond listing can be interpreted as follows:
Bond issuer: Pacific Bell
Coupon rate: 6.55
Maturity date: 2034
Volume: 511
Closing price: 99-4
Net change: 8
Therefore, the correct answer is: The coupon rate is 6.55 and the maturity date is 2034.
learn more about "yield to maturity":- https://brainly.com/question/28033398
#SPJ11
Write an equation to show the total length of the bandages if they are placed end-to-end
There is an image attached btw
The equation that can be written to show the total length of the bandages if they are placed end-to-end is expressed as: 2(5/4) + 6/4 + 3(7/4) + 4(2) + 6(3).
How to Write an Equation for the Total Length?In the image given above that shows a line plot for the set of data representing the length of bandages, we have:
Two 1¼ = 2(5/4)
One 1 2/4 = 6/4
Three 1¾ = 3(7/4)
Four 2 = 4(2)
Six 3 = 6(3)
Thus, the equation that will represent the total length of the bandages can be expressed as:
2(5/4) + 6/4 + 3(7/4) + 4(2) + 6(3)
Learn more about equation on:
https://brainly.com/question/31521223
#SPJ1
LA and LB are vertical angles. If mLA= (4x+6)° and mLB=(2x+18)°, then find the value of x
If a person takes 125 milligrams of a drug, whose concentration
decreases by 30% each hour. how long will it take for the concentration of
the drug in the bloodstream to be 1 milligram?
It takes approximately 10 hours for the drug concentration to decrease.
What is the quadratic formula?We can use exponential decay to model the concentration of the drug in the bloodstream. Let C(t) be the concentration of the drug in milligrams at time t in hours since the person took the drug. Then we have:
[tex]C(t) = 125(0.7)^t[/tex]
where 0.7 is the factor by which the concentration decreases each hour.
We want to find the time t such that C(t) = 1. Substituting this into the equation above, we get:
[tex]1 = 125(0.7)^t[/tex]
Dividing both sides by 125, we get:
[tex]0.008 = (0.7)^t[/tex]
Taking the logarithm of both sides with base 0.7, we get:
[tex]t = log(0.008) / log(0.7)[/tex]
Using a calculator, we can evaluate this expression to get:
t ≈ 10.07
Therefore, it will take approximately 10.07 hours for the concentration of the drug in the bloodstream to be 1 milligram.
Learn more about Mathematics.
brainly.com/question/27235369
#SPJ11
(1 point) Calculate TT, and n(u, v) for the parametrized surface at the given point. Then find the equation of the tangent plane to the surface at that point. O(u, v) = (2u + 0.0 - 40, 8u); u= 3, U =
The equation of the tangent plane to the surface at the point (u,v) = (3,U) is z = x + 34 + U.
To calculate TT, we need to find the partial derivatives of O(u,v) with respect to u and v:
TT = (∂O/∂u) x (∂O/∂v)
= (2, 0, 8) x (0, 0, 1)
= (-8, 0, 0)
To find n(u,v), we normalize TT:
n(u,v) = TT/|TT|
= (-1, 0, 0)
At the point u=3, v=U, O(u,v) = (2u + 0.0 - 40, 8u) = (-34, 24).
To find the equation of the tangent plane, we first find the normal vector to the plane, which is n(u,v) = (-1, 0, 0). Then we use the point-normal form of the equation of a plane:
(-1)(x + 34) + 0(y - 24) + 0(z - U) = 0
-x - 34 + z - U = 0
z = x + 34 + U
Know more about tangent plane here:
https://brainly.com/question/30260323
#SPJ11
Reddy
algebraic expressions with exponents - instruction - level f
) amelia stores her gardening supplies in two cube-shaped boxes. the smaller box has a
volume of 100 in.. amelia wants to know the total volume of both boxes.
s = length (in) of one side of the larger box.
6) write an expression to show the total
volume of the two boxes.
The expression to show the total volume of the two boxes is:
100 + [tex]s^3[/tex] ([tex]in^3[/tex])
We can start by finding the volume of the smaller box using the formula for the volume of a cube:
Volume of smaller box = (length of one side)^3 = 100 in^3
Taking the cube root of both sides, we get:
Length of one side = ∛100 in ≈ 4.64 in
Now, we can use this value to find the volume of the larger box:
Volume of larger box = (length of one side)[tex]^3 = s^3[/tex]
The total volume of both boxes is the sum of the volume of the smaller box and the volume of the larger box:
Total volume = Volume of smaller box + Volume of larger box
Total volume = 100 in [tex]^3 + s^3[/tex]
Therefore, the expression to show the total volume of the two boxes is:
100 + [tex]s^3[/tex] (in[tex]^3[/tex])
To learn more about expression visit:
https://brainly.com/question/30265549
#SPJ11
To conduct a science experiment, it is required to decrease the temperature from 36 c at the rate of 4 c every hour. what will be the temperature 10 hours after the process begins?
To conduct the science experiment, the temperature needs to be decreased from 36°C at a rate of 4°C every hour.
So, after 1 hour, the temperature will be 36°C - 4°C = 32°C. After 2 hours, the temperature will be 32°C - 4°C = 28°C. Continuing this pattern, after 10 hours, the temperature will be 36°C - (4°C x 10) = 36°C - 40°C = -4°C.
However, this temperature is below freezing and unlikely to be accurate for a science experiment.
Learn more about science experiment: https://brainly.com/question/17274244
#SPJ11
Find the missing point of the following parallelogram. (2,4) (6,5) (7,5) (5,3)
Answer:
The missing point of this parallelogram is (6, 5).
Help please I’ve been sick all week so I’m very behind
Answer:
Angle 1 is 77
Angle 2 is 103
Angle 4 is 103
Step-by-step explanation:
Angles that are vertical to each other like 2 and 4, 1 and 3
will always equal each other
since 3 is = to 77, 1 is also = to 77
You can also find the angles by thinking of supplementary angles (180 degrees) Straight angle basically
You see that 3 is 77 and 4 is part of the straight line so it needs to equal 180
so 180-77 it will equal 103.
Hope this helps
Tamika wrote an integer. the opposite of tamika 's integer is -37. which of these statements
about tamika's integer must be true?
i. the integer is -37
ii. the integer has an absolute value of -37
iii. the integer is 37
iv. the integer has an absolute
value of 37
a) i and ii
b) i and iv
c) ii and iii
d) iii and iv
Answer:
D
Step-by-step explanation:
Because the opposite of 37 is -37, III must be true.
Given that absolute values can never be negative, II must be untrue.
Remember the definition of absolute value:
If |x| = x if x >= 0 and |x| = -x if x 0 then IV must be true.
Find the values of x and y that make the quadrilateral a parallelogram
DEFG
5x-4
3y+9
10x-24
2y+16
Answer:
x = 4, y = 7
Step-by-step explanation:
3y + 9 = 2y + 16
y = 7
10x - 24 = 5x - 4
5x = 20
x = 4
values of x is 4 and y is 7
Find the area of a triangle that has sides of 7, 9, and 12 inches
The area of the triangle is approximately 31.3049 square inches.
The area of a triangle can be found using the formula: A = (1/2)bh, where b is the length of the base of the triangle, and h is the height (or perpendicular distance from the base to the opposite vertex).
However, in this case, we don't have the height. Instead, we can use
Heron's formula, which only requires the lengths of the three sides of the triangle:
A = √[s(s-a)(s-b)(s-c)],
where a, b, and c are the lengths of the sides of the triangle, and s is the semiperimeter (half the perimeter): s = (a + b + c)/2.
Using the given values, we have:
s = (7 + 9 + 12)/2 = 14
A = √[14(14-7)(14-9)(14-12)]
A = √[14(7)(5)(2)]
A = √(980)
A ≈ 31.3049 square inches
To know more about area of the triangle, refer here:
https://brainly.com/question/29156501#
#SPJ11
Choose which option shows the plan, which
option shows the front elevation and which
option shows the side elevation of this 3D
shape.
side
front
A
D
G
B
E
H
C
F
Looking at the triangular prism, the options showing the plan, front elevation and side elevation are:
Plan - A Front elevation - F Side elevation - J How to show the elevations ?To show the elevations of a triangular prism, you would need to draw a two-dimensional representation of each of the six faces of the prism, including the top, bottom, and four side faces.
For each face, you would draw the shape of the face, including any dimensions or angles necessary to accurately represent the face. Finally, you would draw lines to show the elevations of each face, indicating how they are connected to form the three-dimensional shape of the prism.
Find out more on front elevation at https://brainly.com/question/30683828
#SPJ1
A cylinder has a radius of 2 ft and a hight of 6 ft. What is the total surface area using 3.14 as pi.
The total surface area of a cylinder is the sum of the areas of its top and bottom circles, along with the area of its lateral surface (the curved surface that connects the two circles).
The formula for the lateral surface area of a cylinder is:
Lateral surface area = 2πrh
where r is the radius of the cylinder, h is the height of the cylinder, and π (pi) is a mathematical constant approximately equal to 3.14.
The formula for the area of a circle is:
Area of circle = πr^2
Using these formulas, we can calculate the total surface area of the cylinder as follows:
Area of top and bottom circles = 2 × π × r^2
= 2 × 3.14 × 2^2
= 25.12 square feet
Lateral surface area = 2 × π × r × h
= 2 × 3.14 × 2 × 6
= 75.36 square feet
Total surface area = Area of top and bottom circles + Lateral surface area
= 25.12 + 75.36
= 100.48 square feet
Therefore, the total surface area of the cylinder is 100.48 square feet.
Question One:
Zahir bought a house 15 years ago, and it is now valued $548 900.00.
Determine the initial value of the home when Zahir purchased it, if it's value
has grown at a rate of 4.8% compounded annually. (2 marks)
Question Two:
Kiran purchases a sofa for $1791.99 (taxes already included). The
department store offers her a promotion of 0% interest with no payments
for one year. If Kiran does not pay the amount in full within one year,
interest will be charged from the date of purchase at an annual rate of
27.93%, compounded monthly.
a) If Kiran does not make any payments, what will the department store bill
her one year after the date of purchase? Show your work. (2 marks)
b) Describe a different compounding period such that the overall cost of the
sofa is lower than if the annual interest rate were compounded monthly. Use
an example to help your explanation. (2 mark)
A. Kiran will be billed approximately $2,284.33 one year after the date of purchase if she does not make any payments.
B. In this case, the overall cost of the sofa would be approximately $2,284.08
How to solve the problemsTo find the initial value of the home when Zahir purchased it, we can use the compound interest formula:
Future Value = Initial Value * (1 + (interest rate))^years
Let Initial Value be P. We are given the Future Value as $548,900, the interest rate as 4.8%, and the number of years as 15.
548,900 = P * (1 + 0.048)^15
Now, we'll solve for P:
P = 548,900 / (1 + 0.048)^15
P ≈ 305,113.48
a. Future Value = Initial Value * (1 + (interest rate / number of periods))^(years * number of periods)
Initial Value = $1,791.99
Interest Rate = 27.93% (0.2793)
Number of periods = 12 (monthly)
Years = 1
Future Value = 1,791.99 * (1 + (0.2793 / 12))^(1 * 12)
Future Value ≈ 2284.33
Kiran will be billed approximately $2,284.33 one year after the date of purchase if she does not make any payments.
b. interest were compounded annually:
Future Value = Initial Value * (1 + interest rate)^years
Future Value = 1,791.99 * (1 + 0.2793)^1
Future Value ≈ 2284.08
In this case, the overall cost of the sofa would be approximately $2,284.08, which is slightly lower than if the interest were compounded monthly ($2,284.33).
Read more on compounding here:https://brainly.com/question/24274034
#SPJ1
To integrate f(x, y, z) = ~ over the region ? consisting of the points (2, Y, 2)
such that
•0≤o≤1,
•0≤y≤2,and
• 0 ≤ 2 ≤ 3x + 4y.
If we want to use the bounds of integration, what kind of integration would we use?
We first integrate with respect to z from 2 to (3x + 4y), then with respect to y from 0 to 2, and finally with respect to x from 0 to 1.
To integrate the given function over the region, we would use triple integration with the bounds of integration as follows:
∫ from 0 to 1 ∫ from 0 to 2 ∫ from 2 to (3x + 4y) f(x, y, z) dz dy dx
This is because the region is defined by the inequalities 0 ≤ x ≤ 1, 0 ≤ y ≤ 2, and 0 ≤ z ≤ (3x + 4y).
Therefore, we first integrate with respect to z from 2 to (3x + 4y), then with respect to y from 0 to 2, and finally with respect to x from 0 to 1.
To learn more about integration, refer below:
https://brainly.com/question/30900582
#SPJ11
